Geodesic
Complex manifolds as families of homotopy algebras
Bellier-Millès, Joan1
1 Université Toulouse III Paul Sabatier, Toulouse, France
Rendiconti del Seminario Matematico della Università di Padova, Tome 140 (2018), pp. 129-172

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We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex structure on a smooth manifold corresponds in this way to a family of algebras indexed by the points of the manifold.

Publié le :
DOI : 10.4171/RSMUP/6
Classification : 18, 32, 53
Mots-clés : Homotopy algebra, complex manifold, operad

Bellier-Millès, Joan 1

1 Université Toulouse III Paul Sabatier, Toulouse, France 
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     title = {Complex manifolds as families of homotopy algebras},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {129--172},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {140},
     year = {2018},
     doi = {10.4171/RSMUP/6},
     mrnumber = {3880215},
     zbl = {1419.18022},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/RSMUP/6/}
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Bellier-Millès, Joan. Complex manifolds as families of homotopy algebras. Rendiconti del Seminario Matematico della Università di Padova, Tome 140 (2018), pp. 129-172. doi: 10.4171/RSMUP/6

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